A block of mass m1=0.560 kg is placed on top of another block of mass m2=0.950 kg, which rests

A block of mass m1=0.560 kg is placed on top of another...

Key Concepts

Free Body Diagram

A free body diagram (FBD) is a simplified representation of an object and the forces acting upon it. It isolates a body to show vector forces like gravity, normal force, friction, and any applied forces, helping to analyze the equilibrium or acceleration of the body in a clear and systematic manner.

Newton's Second Law

Newton's Second Law states that the net force acting on an object is equal to the product of its mass and its acceleration (F = ma). This principle is fundamental in solving dynamics problems as it allows the relationship between forces and the resulting motion to be quantified.

Static Friction

Static friction is the frictional force that resists the initiation of sliding motion between two surfaces in contact. It acts up to a maximum value, which is proportional to the normal force, thereby preventing objects from moving relative to each other until this threshold is exceeded.

Coefficient of Static Friction

The coefficient of static friction is a dimensionless constant that characterizes the frictional properties of the contact surfaces. It quantifies the ratio between the maximum static frictional force and the normal force, and is crucial for determining whether an applied force can overcome static friction to initiate motion.

Systems of Particles

Analyzing a system of particles involves considering the motion and forces acting on multiple interconnected bodies. In such problems, it is often useful to combine the bodies into a single system to determine collective dynamics, or analyze them separately to understand internal interactions like friction between objects.

Transcript

00:03 In this problem, a mass block of 0 .56 kg is kept over a mass of 0 .95 kg block and the two blocks are kept on a frictionless surface.

00:16 So basically friction coefficient of the ground is 0.

00:20 Now a force f is applied in horizontal direction on the lower block in horizontal direction and its magnitude is 3 .46 newton.

00:29 So first of all, we have to draw free body diagram or the force diagram for the upper block and for the two block system.

00:38 So considering this entire two block as a single system.

00:43 So first i'm going to draw free body diagram, which is also known as force diagram for upper block.

01:08 So here two forces that we can easily identify is that the normal reaction force that the lower reaction force that the lower block will apply on the upper block so this normal reaction will be in the perpendicular to the surface of the blocks which will be let us say n1 it is acting in upward direction and weight of the upper block that is m1g will be acting in downward direction now there will be a friction force to identify that in which direction the friction force will be will act for that we can here do some logic now what will be the effect of this friction force so this friction force will try to move the mass in forward direction.

01:51 So with respect to upper block, the lower block is going in forward direction.

01:56 So to avoid this relative motion, the upper block will apply a friction force on the lower block in left direction.

02:04 Now because of newton's second law, the reaction of this friction force on the upward block will be in forward direction.

02:11 Therefore friction force acting on the upper block will be in forward direction.

02:16 And let us say the friction force is f1 so this will be the free body diagram or force diagram for the upper block now what will be the force diagram for combined masses so for the force diagram or combined masses we have to consider these two masses as a single system so at this single system a force f is acting in forward direction weight of the combined system will act in downward direction and there will there will be no friction force force because the friction force is present between the blocks and this force becomes internal force for this combined system and in force diagram we do not show the internal forces we only show the external forces the external surfaces that could have exert friction force is the ground but ground is frictionless therefore there will be no friction force applied on the combined system so what are the forces or the what will be the force diagram for combined system there will be a normal reaction that will be acting vertically upward direction and this reaction force is the reaction force applied by the ground so this is the normal reaction second one will be the weight of the combined system so combined system has mass m1 plus m2 therefore weight will be m1 plus m2 into g and there is no friction force but there is a force that is externally applied f which is of magnitude 3 .46 newton so this will be the force diagram for combined mass.

04:01 So we have to calculate in part b of the problem that what should be the minimum friction coefficient or minimum static friction coefficient such that upper block does not slide or does not slip.

04:15 So what is the condition for slipping? so slip can only occur when the two blocks are moving at different velocity.

04:23 So to avoid the slipping, both of the blocks, both of the blocks.

04:27 Must have same velocity and same acceleration.

04:30 If they have same velocity and same acceleration, then their relative velocity will be zero.

04:35 And if relative velocity is zero, it means that there is no slipping.

04:39 So to calculate the minimum friction coefficient, first of all, we will observe that what should be the combined acceleration if they are under the action of this external force of 3 .46 newton.

04:53 So let us say that their combined acceleration is a...

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